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BANGKOK, Thailand (CNN) -- An estimated 50,000 to 60,000 people rallied Sunday in Bangkok to call for the resignation of Thai Prime Minister Thaksin Shinawatra, with many vowing to remain on the streets until he does.

Sunday's pre-planned protests moved briefly from the initial site, in front of Bangkok's Grand Palace, to the Government House, site of Thaksin's office.

Although some demonstrators went home, others pledged to return to a field in front of the palace overnight. Protesters are hoping to gather the same number for Monday's rallies. Sunday's numbers are based on police estimates.

Thaksin has been accused of corruption and abuse of power, particularly because of the sale of his family's telecommunications firm in Singapore for $1.9 billion -- none of which was paid in taxes.

The billionaire has been accused of undermining the Thai constitution's system of checks and balances and bending government policy to benefit his family's business.

Thaksin, meanwhile, was not in the capital city Sunday, but campaigning in the countryside, traditionally his stronghold.

Last week, he extended an olive branch to opposition parties, offering to meet with Democrat party leader Abhisit Vejjajiva. But Abhisit rejected the offer, saying he has nothing to say to the prime minister.

On Friday, more than 100,000 people gathered in front of the Grand Palace for a rally supporting Thaksin -- many of them bused in from the countryside.

At that rally, Thaksin promised to step down if he gets less than 50 percent of the vote in snap parliamentary elections he has called for in April. He also criticized opposition parties who have said they would boycott that election.

"The opposition chose not to run because they know they are losing," Thaksin told the crowd.

If held in the near future, the ballot would come three years early.

With strong support in upcountry areas, Thaksin was re-elected to a second term last year when his Thai Rak Thai party won 377 of the 500 seats in the House of Representatives.

His main defense against critics is that he enjoys a mandate endorsed by 19 million voters.

-- CNN Bangkok Producer Narunart Prapanya and Senior International Correspondent Mike Chinoy contributed to this story